Preferential duplication graphs
Netta Cohen, Jonathan Jordan, and Margaritis Voliotis
Source: J. Appl. Probab.
Volume 47, Number 2
We consider a preferential duplication model for growing random graphs,
extending previous models of duplication graphs by selecting the vertex to be
duplicated with probability proportional to its degree. We show that a special
case of this model can be analysed using the same stochastic approximation as
for vertex-reinforced random walks, and show that `trapping' behaviour can
occur, such that the descendants of a particular group of initial vertices come
to dominate the graph.
Full-text: Access denied (no subscription
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784910
Digital Object Identifier: doi:10.1239/jap/1276784910
Zentralblatt MATH identifier: 05758488
Mathematical Reviews number (MathSciNet): MR2668507
Bebek, G. et al. (2006). The degree distribution of the generalized duplication model. Theoret. Comput. Sci. 369, 239--249.
Benaïm, M. (1997). Dynamics of stochastic approximation algorithms. In Séminaires de Probabilités XXXIII (Lecture Notes Math. 1709), Springer, Berlin, pp. 1--68.
Benaïm, M. and Tarrès, P. (2008). Dynamics of vertex-reinforced random walks. To appear in Ann. Prob.
Bollobás, B. and Riordan, O. M. (2003). Mathematical results on scale-free random graphs. In Handbook of Graphs and Networks, eds S. Bornholdt and H. G. Schuster, Wiley-VCH, Weinheim, pp. 1--34.
Bonato, A. et al. (2010). Models of on-line social networks. To appear in Internet Math.
Chung, F., Lu, L., Dewey, T. G. and Galas, D. J. (2003). Duplication models for biological networks. J. Comput. Biol. 10, 677--687.
Kumar, R. et al. (2000). Stochastic models for the web graph. In Proc. 41st Annual Symp. on Foundations of Comput. Sci. (Redondo Beach, CA, 2000), IEEE Computer Society Press, Los Alamitos, CA, pp. 57--65.
Pemantle, R. (1988). Random processes with reinforcement. Doctoral Thesis, Department of Mathematics, Massachusetts Institute of Technology.
Pemantle, R. (2007). A survey of random processes with reinforcement. Prob. Surveys 4, 1--79.
Raval, A. (2003). Some asymptotic properties of duplication graphs. Phys. Rev. E 68, 066119, 10 pp.
Volkov, S. (2001). Vertex-reinforced random walk on arbitrary graphs. Ann. Prob. 29, 66--91.